Morphology of an interacting three-dimensional trapped Bose-Einstein condensate from many-particle variance anisotropy

TL;DR

This paper investigates the anisotropic properties of a 3D trapped Bose-Einstein condensate at the many-particle level, revealing differences from mean-field predictions and proposing a new way to classify correlations based on condensate morphology.

Contribution

It introduces a method to analyze anisotropies in BECs at the many-particle level, highlighting differences from mean-field theory and suggesting a new classification of correlations.

Findings

Many-body and mean-field anisotropies differ despite identical densities.

Variance analysis reveals distinct condensate morphologies.

Proposes a classification scheme for correlations based on anisotropy.

Abstract

The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent a wave-packet is non-spherically symmetric. We examine an interacting three-dimensional trapped Bose-Einstein condensate at the limit of an infinite number of particles, and investigate its position, momentum, and angular-momentum anisotropies. Computing the variances of the three Cartesian components of the position, momentum, and angular-momentum operators we present simple scenarios where the anisotropy of a Bose-Einstein condensate is different at the many-body and mean-field levels of theory, despite having the same many-body and mean-field densities per particle. This suggests a way to classify correlations via the morphology of 100\% condensed bosons in a three-dimensional trap at the limit of an infinite number of particles. Implications are briefly discussed.